Results 51 to 60 of about 612 (138)
Nonlinear Engineering, 2019 Fractional calculus and fractional differential equations (FDE) have many applications in different branches of sciences. But, often a real nonlinear FDE has not the exact or analytical solution and must be solved numerically.
Parand K., Nikarya M.
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Studies in Applied Mathematics, Volume 157, Issue 2, August 2026.ABSTRACT We consider the extended Korteweg–de Vries (eKdV) equation as a model for long moderately nonlinear surface water waves and use it to describe the evolution of initial conditions generating solitary waves with and without significant dispersive radiation, as well as cases of pure dispersive radiation without any solitary waves.
Benjamin Martin +2 more
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Developing Hessian–Free Second–Order Adversarial Examples for Adversarial Training
International Journal of Applied Mathematics and Computer ScienceRecent studies show that deep neural networks (DNNs) are extremely vulnerable to elaborately designed adversarial examples. Adversarial training, which uses adversarial examples as training data, has been proven to be one of the most effective methods of
Qian Yaguan +5 more
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Journal of Applied Mathematics, 2012 We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the ...
Jia Liu
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A Matrix‐Free, Scalable, and Robust Implicit Material Point Method
International Journal for Numerical Methods in Engineering, Volume 127, Issue 14, 30 July 2026.ABSTRACT An implicit material point method is presented using a new dynamic relaxation solver, allowing for a simple and efficient quasi‐static formulation that may be readily implemented in existing explicit‐dynamic codes. The use of dynamic relaxation and aggregation is shown to produce an extremely robust material point method scheme, with good ...
Sam J. V. Sutcliffe +5 more
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A splitting preconditioner for the incompressible navier–stokes equations
Mathematical Modelling and Analysis, 2013 In this paper, a splitting preconditioner based on the relaxed dimensional factorization (RDF) preconditioner and the modified augmented Lagrangian (MAL) preconditioner for the incompressible Navier–Stokes equations is presented.
Ze-Jun Hu, Ting-Zhu Huang, Ning-Bo Tan
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A structurally localized ensemble Kalman filtering approach
Quarterly Journal of the Royal Meteorological Society, Volume 152, Issue 778, July 2026 Part A.We derive an inherently localized ensemble Kalman filtering (EnKF) approach, avoiding the need for any auxiliary localization technique. The idea is to first use the variational Bayesian optimization to approximate the (continuous) state analysis probability density function (pdf) by a product of independent marginal pdfs corresponding to small ...
Boujemaa Ait‐El‐Fquih +1 more
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Fast collocation method for a two-dimensional variable-coefficient linear nonlocal diffusion model
Advances in Difference Equations, 2020 In this paper, a fast collocation method is developed for a two-dimensional variable-coefficient linear nonlocal diffusion model. By carefully dealing with the variable coefficient in the integral operator and then analyzing the structure of the ...
Xuhao Zhang, Aijie Cheng
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Shortcuts to Adiabaticity in Krylov Space
Physical Review XShortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies.
Kazutaka Takahashi, Adolfo del Campo
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A Global Krylov Subspace Method for the Sylvester Quaternion Matrix Equation
Journal of New TheoryThis study concerns the Sylvester matrix equation in the quaternion setting when the coefficient matrices as well as the unknown matrix have quaternion entries.
Sinem Şimşek
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